• TASK 1 – QUADRATIC FUNCTIONS The demand function for a new product is p(x) =-4x + 42.5, where x is the quantity sold in thousands and p is the price in thousands. The company that manufactures the product is planning to buy a new machine for the plant. There are three options they can choose from. The cost function for each machine is shown below. Machine A: C(x) =-4.1x + 92.16 Мachine B: Cx) —-17.9х + 29.36 Machine C: C(x) — —8.9х + 55.4 田 1. Determine a revenue function given R(x) =x [p(x)] for Machine A. Show all your work. 2. Determine a profit function given P(x) = R(x) – C(x) for Machine A. Show all your work. 3. How many products, in thousands, does the company need to sell to break even; round your answer(s) to the nearest whole number? Show all your work.

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